1.

Record Nr.

UNINA9910788898703321

Autore

Tu Loring W.

Titolo

Hodge theory and the local Torelli problem / / Loring W. Tu

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , [1983]

©1983

ISBN

1-4704-0689-6

Descrizione fisica

1 online resource (72 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 279

Disciplina

510 s

516.3/52

Soggetti

Curves, Algebraic

Surfaces, Algebraic

Hodge theory

Torelli theorem

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Includes index.

Nota di bibliografia

Bibliography: pages 55-56.

Nota di contenuto

""Table of Contents""; ""Introduction""; ""I. Variation of Hodge structure""; ""Â1. The period map""; ""Â2. The Hodge bundles in the smooth case""; ""Â3. The Hodge bundles when there are singular fibers""; ""The log complex""; ""Relative dualizing sheaf""; ""The canonical extension""; ""Â4. A multiplicative formula for the holomorphic Euler characteristic""; ""Â5. Monodromy""; ""Â6. Mixed Hodge structures and the numerical invariants of a degeneration""; ""6.1. Varieties with normal crossings""; ""6.2. The limiting mixed Hodge structure""; ""6.3. The Clemensâ€?Schmid exact sequence""

""6.4. Genus of a singular curve""""II. Local Torelli for curves""; ""Â7. The case of no singular fibers""; ""Â8. With singular fibers""; ""8.1. First proof: mixed Hodge structure and the topology of the singular fiber""; ""8.2. Second proof: using the relative dualizing sheaf to map X into a projective space""; ""8.3. Third proof: the ample cone on the moduli space M""; ""III. Local Torelli in higher dimensions""; ""Â9. Surfaces with large irregularity""; ""Â10. Threefolds and fourfolds with large irregularity""; ""Bibliography""; ""List of Notations""; ""Index""; ""A""; ""B""; ""C""



""D""""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Y""